The retailer is poised to open a shop in Paris next month and is understood to be close to debuts in Russia, the US, Belgium and Sweden.
All Saints, which has almost 100 branches in the UK and Ireland, including concessions in House of Fraser and Selfridges, already operates outlets in Ibiza, Denmark and Iceland.
The Paris store will open on Rue Etienne. It is also set to open stores in the UK in September in locations including Bristol’s Quakers Friars and Leicester’s Highcross. Openings at Westfield London and in Brown Thomas in Dublin will follow.
Baugur acquired a stake in All Saints from owner Kevin Stanford in 2006 to fund expansion.